I designed the box using CALSOD. I originally oversized the box to 85L to allow for experimentation. A 10" passive radiator from Madisound was included. I tuned it by ear, but I could not find the right sound with the larger 85L box. As a result, I reduced the volume to about 70L. I settled on a passive radiator tuning of 18Hz, tuning by ear, then measuring afterwards. This remains my current setup.
Rather than show the CALSOD results that only show the summed response, I entered the data into Unibox available at the FRD Consortium. The predicted results of various setups are shown below.
The first three graphs show the predicted response characteristics in my current setup that I have used for several years. I have altered the crossover minimally over time, primarily when changing the M/T module or just trying a different crossover. Note that at the driver's power limit (red line), the driver output (gray curve) never exceeds its rated Xmas above 25Hz. This tuning essentially means that the system is power limited, not displacement limited. Below 25Hz the driver is displacement limited. The driver response dip at 30Hz shows the system tuning while the PR response dip at 18Hz shows the PR tuning.
The excursion curves below reveal more. The driver response (dark blue curve) shows the predicted driver response at rated power and again shows the point where it exceeds Xmax, at 25Hz, the point at which its output crosses its Xmax (red line). However, the passive radiator output (light blue curve) shows that it will exceed it's rated displacement at about 45Hz when the driver has rated power applied. I don't think that I've ever come close to applying close to this much power, at or below 45Hz, so the PR limitation is not an issue for my usage.
The impedance curve below shows a fairly standard double-peaked reflex response.
When reviewing the design in Unibox, I experimented some more and set the Fp at 14Hz. I may add some additional weight to tune the PR to 14Hz (as long as the PR can handle the weight) as this seems to extend the reponse a bit better while maintaining the driver's displacement limitation. In fact, it's improved, the driver Xmax limit point going down to 22Hz or so. The reponse looks to be more linear below 20Hz as well, but it is at the cost of output from 32-100Hz, but this may work well depending upon the sensitivity of the rest of the system.
The excursion curves show the improvement in the driver. Even the PR shows improvement to a point. It does not exceed its displacement limitation until about 37Hz, instead of 45Hz for the above noted tuning. In fact, it's improved down to about 22Hz. Above that, the lower tuning is better. Below it and it's the converse. But since there's little music content at 22Hz, it's not an issue at all for my usage.
Consider another example. This one is the same driver and box, but with a PR made by Parts Express. Tuned to the same 14Hz point, but with better Xmax, the driver excursion limits above 20Hz are about the same, only shaped a bit differently. The excursion curves show a different story for this PR, though.
The Parts Express PR has almost twice the Xmax. It can be seen that it doesn't exceed its displacement limitation until about 29Hz. The Madisound PR exceeded its limit at 38Hz, as noted above. So there's close to a full 10Hz of increased headroom for this other PR. At 20Hz the Madisound PR displacement reaches 33mm whereas the Parts Express reaches only 22mm. Of course, this is if either one can even come close to these respective points. This is just to show the better performance overall for the Parts Express PR, it the driver's maximum power handling below 30Hz is to be utilized.
There is one small penalty, though. From about 50Hz down to about 20Hz, the Madisound 14Hz PR system response has about 1db more output, as can be seen in the overlays from the Unibox output files shown below.
This may or may not be significant. It will depend upon the full system response, so consider any system with a PR carefully in all aspects. The cheaper, less dramatic looking Madisound PR has better performance in some respects. It's as I alway say about such a situation, "It depends". That is, it depends upon the design requirements. The Madisound PR satisfies my requirements just fine.
There is another consideration. When the tuning is changed, so is the impedance. The 14Hz tuning results in the impedance below. This will exacerbate problems with the interaction between the crossover and the impedance peaks, primarily to upper peak. This is a real issue, especially with woofers. The crossover components that may be needed to handle this peak can get rather large.
Of course all of the discussion about 14Hz assumes that the PR is capable of holding the weight required to tune it to 14Hz. I believe that both of them are, but have not yet tested this.